The linear Bilevel Programming Problem (BLP) is an instance of a linear hierarchical decision process where the lower level constraint set is dependent on decisions taken at the upper level. In this paper we propose to solve this NP-hard problem using an adaptive search method related to the Tabu Search metaheuristic. Numerical results on large scale linear BLPs are presented.

Abstract We study linear bilevel programming problems, where (some of) the leader and follower variables are restricted to be integer. A discussion on relationships between optimistic pessimistic setting is presented, providing necessary sufficient conditions for them equivalent. new class of inequalities, optimality cuts, introduced. They used derive a single-level non-compact reformulation pr...

This paper is an extension of the K th-best approach [4] for solving bilevel linear programming problems with integer variables. NAZ cut [2] and A-T cut [3] are added to reach the integer optimum. An example is given to show the efficiency of the proposed algorithm.

This paper is devoted to bilevel optimization, a branch of mathematical programming of both practical and theoretical interest. Starting with a simple example, we proceed towards a general formulation. We then present fields of application, focus on solution approaches, and make the connection with MPECs (Mathematical Programs with Equilibrium Constraints).

The family of optimization problems with value function objectives includes the minmax programming problem and the bilevel optimization problem. In this paper, we derive necessary optimality conditions for this class of problems. The main focus is on the case where the functions involved are nonsmooth and the constraints are the very general operator constraints.